K(x)=2x^2+7x-15

Solution for K(x)=2x^2+7x-15 equation:

(K)=2K^2+7K-15

We move all terms to the left:

(K)-(2K^2+7K-15)=0

We get rid of parentheses

-2K^2+K-7K+15=0

We add all the numbers together, and all the variables

-2K^2-6K+15=0

a = -2; b = -6; c = +15;
Δ = b2-4ac
Δ = -62-4·(-2)·15
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*-2}=\frac{6-2\sqrt{39}}{-4}
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*-2}=\frac{6+2\sqrt{39}}{-4}
$